Orthogonal frequency-division multiplexing (OFDM) is an effective technique for combating multi-path fading and for high bit-rate transmission over mobile wireless channels. In OFDM system, the entire channel is divided into many narrow sub-channels, which are transmitted in parallel, thereby increasing the symbol length and reducing the inter-symbol interference (ISI). Channel estimation has been widely used to improve the performance of OFDM systems. It is crucial for diversity combination, coherent detection, and space-time coding. Various OFDM channel estimation schemes have been proposed in the literature:                The least square (LS) or the linear minimum mean square error (LMMSE) estimation is a frequency-domain based channel estimation method that has been proposed in reference [1].        Reference [2] introduced additional discrete Fourier transform (DFT) processing to obtain the frequency response of the LS-estimated channel. In contrast to the frequency-domain estimation method in [1], the transform domain estimation method uses the time-domain properties of channels.        Reference [3] describes a channel estimation method based on the discrete cosine transform instead of the DFT.        
However, in many applications, such as orthogonal frequency division multiple access (OFDMA) system, only channel estimates of a part of the complete frequency response are available (since each user only accesses part of the available spectrum), and the estimate of the channel impulse response in the time domain cannot be obtained from the conventional DFT based method. After the inverse discrete Fourier transformation (IDFT) of the partial frequency response, the channel impulse response will leak to all taps in the time domain. Since the noise and leakage power are mixed up, the conventional DFT method will not only eliminate the noise, but also loose the useful but leaked channel power.